The present invention relates to image segmentation, and more particularly, to image segmentation using radial basis functions (RBFs).
Since the introduction of active contour methods, they have been successfully used in computer vision applications. Such active contour methods have been used in many important applications, such as image segmentation, 3D scene reconstruction, and object tracking. One reason why active contours have been used so successfully is that they provide a structured approach, via energy minimization, to deform a contour or surface.
In the context of image segmentation, active contours deform based on various image-based and internal forces so that the contour's edges match object or region boundaries in the image, while maintaining smoothness. The smoothness, or regularization terms, provide robustness to noise while providing a measured approach to handling missing or low-confidence data. A typical application of an active contour will start with an initial contour, which is then iteratively deformed until it converges to a solution that balances the forces acting on the contour. Typically, these forces result from analytical expressions that are derived using variational calculus applied to an energy minimization problem. However, it is possible to define the forces directly without using an energy formulation.
In the convention active contour techniques, earlier methods represented the contour using a topologically fixed parametric representation, such as a polyline, spline, etc., specified by a fixed number of control points. Such representations are simple and efficient to implement, however, they lack straightforward mechanisms for topological control. Often in segmentation problems, the topology of the problem is unknown a priori, and the contour must break apart or merge during the evolution of the contour. Such topological changes cannot traditionally be performed by active contours using a topologically fixed parametric representation. Although various methods for providing topological changes have been proposed, the implementation of such methods is complicated and not natural to active contour techniques based on parametric representations.
More recent techniques use implicit active contours, or level-set methods, which represent the contour as a level set of a higher dimensional embedding function. The primary advantage of this representation is that topological changes occur naturally in the evolution of the contour. By manipulating the embedding function, the level set that represents the contour can innately split or merge without requiring any specialized implementation to handle topological changes. However, the embedding function must be updated on a dense set of points, which requires a significant amount of storage, even when using efficient narrowband techniques.
Recently introduced methods attempt to combine some of the advantages of explicit and implicit active contours through the use of radial basis functions (RBFs), or unstructured point clouds. Such methods model an implicit function defining an active contour as a superposition of RBFs. The RBFs define a set of points (each point representing an RBF), from which the embedding function can be calculated. The points (RBFs) are moved (and correspondingly, the embedding function is updated) in order to deform the active contour to solve a segmentation problem. These approaches have been demonstrated to provide the topological flexibility of level set methods with the low storage requirements of parametric representations, and provide flexibility in terms of RBF placement and interaction.